{
  "abstract": "We extend Cuenin's compact-manifold spectral bounds for Schrödinger operators with complex potentials to a general pseudodifferential setting. More precisely, we study operators \\(P+V\\), where \\(P\\) is a positive self-adjoint elliptic classical pseudodifferential operator of positive order and \\(V\\) is complex-valued. The main analytic input is a resolvent principle showing that spectral cluster estimates for \\(P\\) imply \\(L^p\\)-\\(L^{p'}\\) resolvent estimates along suitable complex curves. Combined with Sogge's spectral cluster bounds, this yields exterior-region resolvent estimates extending those of Krupchyk and Uhlmann; we also prove direct resolvent bounds in the interior region. On Zoll manifolds, we discuss the sharpness of the resulting spectral bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10127",
  "author_total": 1,
  "authors": [
    {
      "name": "Eduard Stefanescu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/by98cxhxetr59.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10127",
  "fulltext_url": null,
  "id": "by98cxhxetr59",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10127",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7212167552",
  "pdf_url": "https://arxiv.org/pdf/2609.10127",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/by98cxhxetr59.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.10127",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10127"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Resolvent bounds and eigenvalue estimates of generalized Schrödinger operators with complex potentials on compact manifolds",
  "title_text": "Resolvent bounds and eigenvalue estimates of generalized Schrödinger operators with complex potentials on compact manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/by98cxhxetr59",
  "venue": "arXiv",
  "versions": []
}